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326                              CHEMICAL ENGINEERING
readily but graphite, 2.09 to 2.229; molybdenite, 4.44 to 4.80; and gray copper, 4.50 to 5.56; also float readily as also do many organic compounds. The specific gravity of quartz and earthy materials and gangue ranges from 2.4 to not more, ordinarily, than 3.5, quartz being 2.67.
If more than one substance is to be concentrated out of a matrix or gangue the difficulties of separating one from the other and the gangue are very much greater than if a single substance is to be separated from gangue. If the plurality of substances to be concentrated is finely disseminated through the gangue or closely mixed with one another a concentration problem is presented which will either present insuperable difficulties in solution or lead to high costs for plant and operation. A microscope can often be used profitably here.
In testing for a flowsheet portions of the material to be treated are crushed to various sizes which an inspection before reduction would indicate as being the points where either (a) a sufficient quantity of concentrate can be obtained or (6) clean tailings can be produced. If clean tailings can be produced following preliminary crushing operations, great savings can be effected in the finishing treatment as the roughing concentration will reduce the quantity of middling material which has to be further ground before being submitted to the final concentrating operations. Hand-sorting tests should also be made to determine whether clean waste can be made. Concentrating by machinery used to be considered to begin in the neighborhood of 2 in. but 1 in. is today nearer the extreme upper limit at which concentration begins.
The best range for hand sorting is usually from 3 to 1 in. Above a piece of 3-in. size the difficulty of handling the pieces with despatch becomes increasingly difficult owing to their weight. Below 1-in. size the tonnage made per man by hand removal becomes too small ordinarily to make sorting operations profitable. Such small pieces are also difficultly recognizable. The successful employment of hand sorting largely depends upon the sorter being able to make an instant decision as to whether the fragments passing before him are ore or waste. In sorting the material of least tonnage should be removed. If there be but little ore in the stream passing the sorter the ore should be taken out. And this is the usual problem. Where there is only a little waste to be removed common sense will indicate that the sorting operation may be left out of the mill scheme.
The scheme of the flowsheet following the preliminary concentration consists in regrinding the middling products and submitting them to further concentrating operations. It will be evident that the tailings from the preliminary operation can be higher than those from the final operations. The amount of valuable substance which can be left go to waste in the tailings depends on the individual ore. It is best to err on the commercial side, that is, to leave in tailings more valuable substance than would be necessary if the most refined methods were employed. Each successive reduction and retreatment method is increasingly more expensive and at the same time the percentage recoveries diminish.
Jigs and Jigging.—The principle of Archimedes which states that a body in a fluid loses a weight equal to the weight of the fluid displaced enables one to write a formula for the unbalanced force acting on a fragment of material subsiding in a fluid. The unbalanced force is Vw(s' — s), where V is the volume of the grain, w the weight of a unit of water and sf and s the specific gravities respectively of the solid and fluid in terms of water. The acceleration of such a pars' — s tide if there were no fluid resistance would be g —j~ and quite evidently if there